The Weak Isolated Minimality Of The Variational Inequality’s Solutions In Banach Space And The Existence Of Half Strongly Monotone Variational Inequality’s Solution

variational inequality plays an important role in the field of economic equilibri-um, optimal control, differential equation and game theory etc. In the first part of this thesis, aiming at the variational inequality problems in Banach space, we firstly introduce a concept of weak sharp minima, then discuss the relationship among the original gap function, the dual gap function and weak sharp minima. Finally, using the projection theorem, we give the necessary conditions and sufficient conditions for the existence of weak sharp minima.In the second part of this thesis, we consider set-valued variational inequality problems. We firstly introduce a concept of semi-pseudomonotone. then compare the difference between semi-pseudomonotone property and other monotone proper-ty. Under the condition of semi-pseudomonotone, we establish an theorem of the nonemptiness and boundedness of the solution set, and give sufficient conditions for the existence of error bounds with Holder order for the solution set.